Convergence and quasi-optimality of adaptive finite element methods for harmonic forms
Sign Up to like & getrecommendations! Published in 2017 at "Numerische Mathematik"
DOI: 10.1007/s00211-016-0862-6
Abstract: Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework also relies extensively on accurate computation… read more here.
Keywords: finite element; adaptive finite; element methods; harmonic forms ... See more keywords
Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation
Sign Up to like & getrecommendations! Published in 2022 at "Numerische Mathematik"
DOI: 10.1007/s00211-021-01259-8
Abstract: Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices have to be computed… read more here.
Keywords: boundary element; wave equation; cross approximation; approximation ... See more keywords
Weak maximum principle of finite element methods for parabolic equations in polygonal domains
Sign Up to like & getrecommendations! Published in 2024 at "Numerische Mathematik"
DOI: 10.1007/s00211-025-01453-y
Abstract: The weak maximum principle of finite element methods for parabolic equations is proved for both semi-discretization in space and fully discrete methods with k-step backward differentiation formulae for k=1,…,6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}… read more here.
Keywords: weak maximum; maximum principle; methods parabolic; principle finite ... See more keywords
Expandable Parallel Finite Element Methods for Linear Elliptic Problems
Sign Up to like & getrecommendations! Published in 2020 at "Acta Mathematica Scientia"
DOI: 10.1007/s10473-020-0218-2
Abstract: In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are… read more here.
Keywords: finite element; linear elliptic; parallel finite; expandable parallel ... See more keywords
Finite Element Methods for a System of Dispersive Equations
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-018-0767-x
Abstract: The present study is concerned with the numerical approximation of periodic solutions of systems of Korteweg–de Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate two types of schemes that differ… read more here.
Keywords: finite element; system; dispersive equations; methods system ... See more keywords
Hybridization and stabilization for hp-finite element methods
Sign Up to like & getrecommendations! Published in 2019 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2018.09.017
Abstract: Abstract In this paper various hybrid hp-finite element methods are discussed for elliptic model problems. In particular, a stabilized primal-hybrid hp-method is introduced which approximatively ensures continuity conditions across element interfaces and avoids the enrichment… read more here.
Keywords: stabilized primal; hybrid method; element methods; primal hybrid ... See more keywords
Numerical Analysis of Fully discrete Finite element Methods for the stochastic Navier-Stokes Equations with Multiplicative Noise
Sign Up to like & getrecommendations! Published in 2021 at "Applied Numerical Mathematics"
DOI: 10.1016/j.apnum.2021.07.018
Abstract: Abstract Previous work on the stability and convergence analysis of the finite element methods for the deterministic Navier-Stokes equations was carried out under the uniqueness condition. In this paper, the corresponding results of fully discrete… read more here.
Keywords: stokes equations; element methods; fully discrete; finite element ... See more keywords
Compatible-strain mixed finite element methods for 2D compressible nonlinear elasticity
Sign Up to like & getrecommendations! Published in 2017 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2016.09.047
Abstract: Abstract In this paper, using the Hilbert complexes of nonlinear elasticity, the approximation theory for Hilbert complexes, and the finite element exterior calculus, we introduce a new class of mixed finite element methods for 2D… read more here.
Keywords: finite element; mixed finite; nonlinear elasticity; element methods ... See more keywords
Interface-penalty finite element methods for interface problems in H1, H(curl), and H(div)
Sign Up to like & getrecommendations! Published in 2020 at "Computer Methods in Applied Mechanics and Engineering"
DOI: 10.1016/j.cma.2020.113137
Abstract: Abstract In this article, interface-penalty finite element methods are proposed to solve interface problems in H 1 , H ( curl ) , H ( div ) spaces on unfitted tetrahedral meshes. The transmission conditions… read more here.
Keywords: interface penalty; finite element; element methods; interface ... See more keywords
Computation of electric field inside substations with boundary element methods and adaptive cross approximation
Sign Up to like & getrecommendations! Published in 2018 at "Engineering Analysis With Boundary Elements"
DOI: 10.1016/j.enganabound.2018.03.002
Abstract: Abstract Power system substations and HV power lines are sources of electric and magnetic fields of industrial frequency. Guidelines for permissible electric and magnetic field strengths regarding human exposure and electromagnetic compatibility (EMC) are provided… read more here.
Keywords: computation; field; element methods; adaptive cross ... See more keywords
Stabilized equal lower-order finite element methods for simulating Brinkman equations in porous media
Sign Up to like & getrecommendations! Published in 2024 at "International Journal of Computer Mathematics"
DOI: 10.1080/00207160.2024.2343102
Abstract: This paper demonstrates the mixed formulation of the Brinkman problem using linear equal-order finite element methods in porous media modelling. We introduce Galerkin least-squares (GLS) and least-squares (LS) finite element methods to address the incompatibility… read more here.
Keywords: finite element; order finite; element methods; porous media ... See more keywords